Biological control for predation invasion based on pair approximation

Zhiyin Gao; Sen Liu; Weide Li; Zhiyin Gao; Sen Liu; Weide Li

doi:10.3934/mbe.2022480

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 10252-10274. doi: 10.3934/mbe.2022480

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Biological control for predation invasion based on pair approximation

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
2.
Center of Applied Mathematics of Gansu, Lanzhou 730000, China
3.
Center for Data Science, Laboratory of Applied Mathematics and Complex System, Lanzhou University, Lanzhou 730000, China

Academic Editor: Sanling Yuan

Received: 25 May 2022 Revised: 26 June 2022 Accepted: 11 July 2022 Published: 20 July 2022

Biological invasions have been paid more attention since invasive species may cause certain threats to local ecosystems. When biological control is adopted, selecting control species for effect better becomes the focus of latest studies. A food web system, with one native species, one invasive species as predator, and one introduced control species preying on both native and invasive species, is established based on pair approximation, in which the spatial landscape of biological invasion and control is concerned, and the local and global dispersal strategies of invasive species, in addition to the predation preferences of control species for native and invasive species, are considered. The influence of the initial density and initial spatial structures of the control species is investigated and the effects of control species releasing time are analyzed. Generally, the earlier the species introduction, the better the control effect, especially for invasive species dispersing globally. Interestingly, too low control species predation preference for native species can lead to unsuccessful introduction, while too much predation preference will have a weak control effect. The larger the control species predatory preference for invasive species is, the more conducive it is to biological control. The extinction of the invasive species is closely related to the initial density and concentration of the control species. This study gives some insights on selecting control species, its appropriate releasing time, and the density and spatial aggregation of it. Some real-life examples are elaborated on, which provides references for biological invasion control.
- biological invasion,
- biological control,
- pair approximation,
- cellular automata,
- predation preference,
- dispersion strategy
Citation: Zhiyin Gao, Sen Liu, Weide Li. Biological control for predation invasion based on pair approximation[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10252-10274. doi: 10.3934/mbe.2022480

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Abstract

Biological invasions have been paid more attention since invasive species may cause certain threats to local ecosystems. When biological control is adopted, selecting control species for effect better becomes the focus of latest studies. A food web system, with one native species, one invasive species as predator, and one introduced control species preying on both native and invasive species, is established based on pair approximation, in which the spatial landscape of biological invasion and control is concerned, and the local and global dispersal strategies of invasive species, in addition to the predation preferences of control species for native and invasive species, are considered. The influence of the initial density and initial spatial structures of the control species is investigated and the effects of control species releasing time are analyzed. Generally, the earlier the species introduction, the better the control effect, especially for invasive species dispersing globally. Interestingly, too low control species predation preference for native species can lead to unsuccessful introduction, while too much predation preference will have a weak control effect. The larger the control species predatory preference for invasive species is, the more conducive it is to biological control. The extinction of the invasive species is closely related to the initial density and concentration of the control species. This study gives some insights on selecting control species, its appropriate releasing time, and the density and spatial aggregation of it. Some real-life examples are elaborated on, which provides references for biological invasion control.

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